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August 22, 2025Open Access

Congruency, Homomorphism and Isomorphism on Autometrized Algebras

Key Points

Congruence relations form a complete sublattice of equivalence relations in normal autometrized algebras, emphasizing their structure.
Key findings reveal that congruence-permutable autometrized algebras also exhibit congruence-modular traits, showcasing deep algebraic ties.
This study analyzes congruence relations, homomorphisms, and isomorphisms to define fundamental properties in autometrized algebra.
The findings suggest the kernel of a homomorphism qualifies as a congruence relation, illuminating connections between these concepts.

Abstract

This paper presents a study of congruence relations on autometrized algebras. We demonstrate that in a normal autometrized algebra, which satisfies certain conditions, the set of all congruence relations forms a complete sublattice within the set of all equivalence relations. Furthermore, we investigate the property that a congruence-permutable autometrized algebra is also congruence-modular. We also explore several fundamental properties related to congruence relations. Additionally, we introduce the kernel of a homomorphism and establish that it is a congruence relation. Lastly, we examine the homomorphism, isomorphism, and correspondence theorems of autometrized algebra using the concept of congruence.

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